The dynamic modulus (E*) of hot-mix asphalt mixtures is one of the most laborious and time-consuming material parameters to measure in the laboratory. It involves expensive, specialized equipment and expertize that are not readily available in most laboratories. Consequently, several efforts have been devoted to E* prediction models. Unfortunately, developing these prediction models is complex because of the numerous contributory factors and their non-linear influence on E* values. Moreover, such models are not able to prioritize or screen the major factors influencing the E* values. This study presents a new framework for analyzing the dynamic modulus influencing factors by adopting two modeling approaches. First, deep residual neural networks (DRNNs) for non-parametric approaches are used to improve the E* prediction capabilities and derive deep insight into the contributory parameters' effect on the E* value. Second, the well-known Witczak 1–40D prediction equation is used as a representative of the classical statistical modeling approach. In the validation of the models, a comprehensive laboratory database is utilized to account for all significant contributory parameters, such as binder characteristics, volumetric properties, mixture gradation, and testing circumstances parameters. Then, the performance is assessed using typical performance metrics. Lastly, intensive global sensitivity analysis (GSA) is undertaken with the assistance of Latin Hypercube Simulation. Three distinct GSA methods are used to emphasize the influence of each contributory factor on the value of E* in actual practice while reducing the possibility for result distortion owing to correlations between contributory variables. Performance metrics of the DRNNs and the Witczak 1–40D prediction models give the GSA conclusions high credibility. The GSA reveals that, among all possible inputs, the binder content, shear modulus, voids in the mineral aggregates, and temperature are the most significant factors in determining the E* value.